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Finding the Third Proportional to 205,140 and 431,014

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Solution

The third proportional to 205,140 and 431,014 is: 905,591.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,140 : 431,014 = 431,014 : x
  2. Step 2: Convert to fraction form
    205,140/431,014 = 431,014/x
  3. Step 3: Cross multiply
    205,140x = 431,014 × 431,014
  4. Step 4: Simplify right side
    205,140x = 185,773,068,196
  5. Step 5: Solve for x
    x = 185,773,068,196/205,140
  6. Step 6: Final answer
    x = 905,591.64

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.